Stabilizing control of Markovian jump systems with sampled switching and state signals and applications

This article addresses the stabilization problem of continuous-time Markovian jump systems (MJSs). Because of both switching and state signals sampled, a novel system with an exponential matrix characterizing the sampling effects is developed. It is used to be an auxiliary system and plays important roles in system analysis and synthesis. Sufficient stabilization conditions are presented and fully consider the sampling rate. The applications of established methods and results are applied to networked control in the presence of denial-of-service (DoS). The frequency and duration of DoS attacks ensuring stability of the closed-loop system are characterized. Meanwhile, more special situations about particular transition rate matrix, sampling logic and improved mode-dependent controller are considered respectively. The analysis results are significant and bring an important method to study the control for MJSs with sampled switching and state signals. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.

Automated summary

This article addresses the stabilization problem of continuous-time Markovian jump systems (MJSs) by developing a novel system with an exponential matrix characterizing the sampling effects. Sufficient stabilization conditions fully considering the sampling rate are presented, with applications to networked control in the presence of denial-of-service (DoS) attacks characterized. Special situations regarding particular transition rate matrix, sampling logic, and improved mode-dependent controller are also considered. The analysis results are significant and provide an important method for studying the control of MJSs with sampled switching and state signals. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.